Assessment: Optimization
Name: kc? Section #2
Complete the following problems.
1. A closed rectangular shipping crate is to be constructed with a square
base. The material for the two square ends (base and top) costs $5 per
square foot and the material

Name: _
MAC1140 Precalculus
Final Exam Sample Test
12/7/2016
Part I: No calculators may be used, show appropriate work/reasoning in the space provided.
1. Below is a graph of the function h(x), find each limit as listed below. If the limit does not
exist,

Name: _
MAT1033C Intermediate Algebra
Final Exam Sample Test
12/7/2016
1. The school that Addison goes to is selling tickets to a concert performance. On the first day
of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a tota

Lecture 6: Limits, Velocity and Tangent Lines
(Sections 2.1 and 2.2)
Recall that the
average velocity =
Note that velocity has direction and speed = |velocity|.
Now try the following example before class:
ex. A turtle is moving along a path so that its di

Lecture 31 Areas (Section 5.1)
y = f(x)
a
b
How to find the area of the region that lies under the curve
y = f (x) from a to b?
ex. Let f (x) = x and consider the area beneath the
graph of the function on [0, 4].
2
y=
x
4
Let Rn be the sum of the areas of

Lecture 33 The Fundamental Theorem of
Calculus (Sections 5.3 and 5.4)
ex. Given the function y = f (t) = 4t:
y = 4t
Now consider the function of x for x 0 defined by
Z x
4t dt.
A(x) =
0
For any given x, we know that A(x) gives the area of the
region bound

Class Notes - Sections 4.6-4.7, Optimization
Classic Example: A farmer as 2400 feet of fencing and wants to fence off a
rectangular field that borders a straight river. He needs no fence along the
river. What are the dimensions of the field that has the l

Class Notes - Section 4.3, Derivatives and the Shapes of Curves
How do we determine where a function is increasing/decreasing?
Increasing/Decreasing Test
1. If f 0(x) > 0 on an interval, then f is increasing on that interval.
2. If f 0(x) < 0 on an interv

Class Notes - Section 4.2, Maximum and Minimum Values
Applications:
1. What is the shape of a can that minimizes manufacturing costs?
2. At what price should a business sell its product in order to maximize revenue?
3. What is the maximum concentration of